It is not required to have SYSDBA privileges to access RMAN (the
standard backup utility for Oracle). There is a specific right called
BACKUP ANY TABLE that can act as a substitute privilege. There are
even a few packaged roles on some versions of Oracle that grant you
the access you need. Of course if you don't have the privileges to
grant yourself the privileges....

Per Oracle 11g Docs:
RMAN connections to a target or auxiliary database require the SYSDBAprivilege
BACKUP ANY TABLE
Use the Export utility to incrementally export objects from the schema of
other users.